The Colorado Democrat needs the cash, but the visit is giving Republicans, including challenger U.S. Rep. Cory Gardner, another chance to link the first-term senator with the White House — an association that even Udall has taken steps to temper.

US President Barack Obama and Senator Mark Udall play golf on the first hole at Andrews Air Force Base in Maryland, on May 6, 2013. (Saul Loeb, AP)

In a January interview with CNN, Udall dodged questions on whether he would campaign with Obama. No campaign events are planned this visit, although a Udall spokesman said the senator would "welcome" the chance to appear with Obama.

"We're hoping to welcome past, present and/or future presidents to the state to connect with voters and speak to Mark's record of always fighting to do right by Colorado," wrote Chris Harris, a Udall spokesman.

Obama has motivation to help Udall as well. For Democrats to keep control of the Senate — and give his presidency any chance of getting anything done in his last two years — he needs swing-state senators such as Udall to win.

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Whether that means Obama returns to Colorado again, or simply stays away, remains to be seen.

That's bad news for Udall, said one political expert, because presidential approval is the "one of the single most important factors" in determining whether members of the president's party will win during a mid-term election year.

"It matters enormously," said Larry Sabato, director of the Center for Politics at the University of Virginia.

The reason, he said, is that voter turnout in mid-term years is traditionally less robust than in presidential years. And so lawmakers need an excited base — as well as few content independents — to overcome the historical dissatisfaction that hinders incumbent members of the president's party during a midterm election.

"What Udall has to worry about ... is that the Democratic coalition has eroded," Sabato said.

A lack of enthusiasm among young voters and minority voters — exacerbated by the Obama's poll numbers — is a major obstacle for Udall, and "identifying those voters and getting them out to vote" is critical for the Colorado Democrat, Sabato said.

To do that takes money, which is why Wednesday's fundraiser is a smart play, he added.

Udall is "already connected at the hip [to Obama]. It's not going to hurt to connect to Obama in the wallet," Sabato said.

Indeed, Republicans have not hesitated to make their relationship an issue this campaign.

Ahead of Wednesday's fundraiser, Ryan Call, state GOP chairman, accused Udall of being a "rubber stamp" for the administration and as evidence he pointed to Udall's past votes in favor of the Affordable Care Act — also known as Obamacare — and against the Keystone pipeline.

"He has been carrying Obama's water in the Senate," Call said.

But Udall's spokesman argued that the senator's legislative record is more nuanced.

"It really comes down to [the] issue," Harris said.

He highlighted Udall's efforts to safeguard U.S. privacy rights from overreach by the National Security Agency, as well as the fact that Udall was the first Senate Democrat to call for the resignation of Eric Shinseki, now the former head of the U.S. Department of Veterans Affairs.

Although Udall supports the president on causes such as immigration reform, "on other issues he has made it clear that he is frustrated with the White House and its leadership," said Harris, including the "bungled" rollout of the administration's health care website.